Sampling From Variational SU(2)-Symmetric Quantum States

In condensed matter physics, simple spin models with continuous non-abelian symmetries can give rise to interesting phases of matter. In order to further explore the phenomenology of these quantum systems, it is critical to develop scalable variational methods that exploit the presence of these symmetries. Here, we discuss spin-rotation symmetry and a corresponding SU(2)-symmetric architecture for representing quantum states (Vieijra and Nys, 2021). We implement the first three layers of the architecture and benchmark it on small systems, and compare against architectures that do not enforce the full SU(2) symmetry. Lastly, we suggest next steps, such as testing the architecture at scale for two-dimensional lattice models.